There is no such thing as "regular molding", there are many ways this could have been done. To say "regular molding" really isn't enough information.

Are you saying your existing molding is three inches wide, and if so, what is it made of?

You can get several types of transition moldings for this purpose.

You may also want to continue your posts in your original thread so as to save confusion and keep from having several different questions all in different threads. One thread would make it much easier to follow your project.

Tell us more about your existing transition and we'll help you with an answer.